含研究報告撰寫范例英文

CALDER?NTECHNIQUEBASEDINTEGRALAMasterThesisSubmittedUniversityofElectronicScienceandTechnologyofAdvisor: School 本人所呈交的是本人在導(dǎo)師指導(dǎo)下進(jìn)行的研究工作外，中不包含其他人已經(jīng)或撰寫過的研究成果，也不包含為獲得電子科技大學(xué)或其它教育機(jī)構(gòu)的或而使用過的材料。與我一同工作的對本做的任何貢獻(xiàn)均已在中作了明確的作者簽名 日期 本作者完全了解電子科技大學(xué)有關(guān)保留、使用的規(guī)定保留并向國家有關(guān)部門或機(jī)構(gòu)送交的復(fù)印件和磁盤，允許被查閱和借閱。本人電子科技大學(xué)可以將的全部或部分內(nèi)容編入有關(guān)數(shù)據(jù)庫進(jìn)行檢索，可以采用影印、縮印或掃描等保存、匯編。（的在后應(yīng)遵守此規(guī)定作者簽名 導(dǎo)師簽名日期 RevealedbytheCalder?nrelationandtheCalder?nidentitiesinelectromagnetictheory,thepropertiesandrelationofdifferentintegraloperatorsinthecomputationalelectromagnetics(CEM)areutilizedtoconstructtheCalder?npreconditioningtechniques,whichareappliedintheintegral-equation-basedmethodsinthisthesis.Athoroughandsystematicresearchhasbeen plishedtocovertheCalder?npreconditioningtechniquesfortheperfectelectricconductor(PEC)andthedielectriccases.ForthePECcase,theCalder?npreconditioningfortheelectric-fieldintegralequation(EFIE)atmid,low,andhighfrequenciesareconstructedandstudied.Forthedielectriccases,the preconditioningforthePoggio-Miller-Chang-Harrington-Wu-Tsai(PMCHWT)integralequationareinvestigated,andtheCalder?ntechniquefortheN-Müllerintegralequationisdeveloped.Moreover,theaccuracyimprovingtechniqueforthesecond-kindFredholmintegralequationforbothPECanddielectriccasesisalsostudiedinthisthesis.…Keywords:Electromagneticscatteringandradiation,surface-integral-equation-basedMethods,Calder?npreconditioningmethods,numericalaccuracy,Fred-holmintegralequationsofthesecondkindChapter1 ResearchBackgroundand Stateof ContentsandInnovationsofthe Outlineofthe Chapter2Theoretical IntegralEquationsin 270MHzPlanWave TheSolutionofIntegralEquationsin GeneralPrincipleoftheMethodof GeometricalModelingandDiscretizationof PlanarTriangular CurvilinearTriangular TheChoiceofBasis PlanarRWGBasis CurvilinearRWGBasis TheSolutionofMatrix Direct Iterative Chapter3Calder?nPreconditioneratMid Calder?nRelationandCalder?n Calder?nPreconditioneratMid Numerical Chapter4Calder?nPreconditioningTechniqueforN- N-MüllerIntegral TheDerivationofN-Müller TheDiscretizationofN-Müller Numerical Chapter5 Concluding Future ResearchResultsObtainedDuringtheStudyforMaster ①①Chapter1ResearchBackgroundandIntegral-equation-basednumericalmethodscombinedwithfastalgorithmsarecapableofsolvingelectromagneticproblemsofcomplexstructuresandmaterialpropertieswithagoodaccuracyandahighefficiency.Theyarewidelyusedinavarietyofengineeringapplications,suchastheefficientysisofthreedimensionalradarscatteringproblems,thesimulationoftheinputimpedanceandtheradiationpropertiesofantennasystems,thecalculationoftheinputresponseandthetransmissionefficiencyofmicrowavecircuits,theevaluationoftheelectromagneticinterference(EMI)betweencomplexelectromagneticsystems,andthecomputeraidedelectromagneticcompatibility(EMC)designs.Theversatility,capability,accuracyandefficiencyoftheintegral-equation-basedmethodshavemadethemanimportantandcosteffectiveapproachintheysisanddesignofelectromagneticproblemsandapplications.…StateofFromthe1960s,thenumericalmethodsofelectromagneticysishavebeenfastdevelopedbecauseoftheirversatilityandflexibility.Manywell-knownnumericalmethodshavebeenintroducedduringthattime,includingthefiniteelementmethod(FEM)[1]andthefinitedifferencetime method(FDTD)[2,3],whicharebasedonthesolutiontotheMaxwell’sequationsindifferentialform,andthemethodofmoments(MoM)[2,4-6],whichisbasedonthesolutiontotheMaxwell’sequationsinintegralform.Especiallyfrom1990s,withthefastdevelopmentsofhighperformancecomputingsystems,thetheoriesandmethodsofcomputationalelectromagneticshavebeenadvanceddramatically.Theincreasesoftheclockspeedandthememorysizeofcomputersystemsandthedevelopmentsofhighlyefficienectromagneticcomputingalgorithmsmakethenumericalmethodscapableofsolvingelectromagneticengineeringproblems.①…ContentsandInnovationsoftheBasedontheCalder?nrelationandtheCalder?nidentities,thisthesishasdevelopedseveralCalder?npreconditioningtechniquesandinvestigatedtheirapplicationsintheintegral-equation-basedcomputationalelectromagneticmethods.TheresearchcontenthascoveredtheCalder?npreconditioningtechniquesfortheperfectelectricconductor(PEC)anddielectriccases.ForthePEC①case,theCalder?npreconditionsatmid,low,andhighfrequenciesareinvestigated.Forthedielectriccase,theCalder?npreconditioningtechniquesforthePMCHWTandN-Müllerintegralequationsaredeveloped.Thenumericalaccuracyofthesecond-kindFredholmintegralequationsareinvestigatedandimprovedinthisthesis.…OutlineoftheThisthesis anizedas…Chapter2TheoreticalInthischapter,thegeneralmethodsofconstructingthecommonlyusedintegralequationsinelectromagneticsareintroducedbasedonthesurfaceequivalenceprincipleandthevolumeequivalenceprinciple.…IntegralEquationsinIntheintegral-equation-basedcomputationalelectromagneticmethods,theunknownfunctionsintheelectromagneticproblemssuchasthescatteringorradiationfieldsaremodeledintermsoftheequivalentsurfaceorvolumeelectric/magneticsourcesbyapplyingthesurfaceorvolumeequivalenceprinciples,respectively.…270MHzPlanWaveInordertoinvestigatetheitsperformanceinhandlingelectricallyverylargeproblemswithoveronemillionunknowns,thesamenumericalexampleisrepeatedagainbyincreasingthefrequencyto270MHz,andkeetheincidentangleandpolarizationoftheplanewaveunchanged.Tohaveabetterinsight,thememoryconsumptionandCPUtimerequirementsoftheEFIE,theCP-CFIE(0.8),andtheCP-AEFIEalgorithmsaregiveninTable2-1.Table2-1ComparisonofComputationalDataofDifferentTotalMemoryCPUSetupSolutionIter.Tol.AllthecalculationsarecarriedoutonaHPZ400workstationwithaFedora10operatingsystem.…TheSolutionofIntegralEquationsinGeneralPrincipleoftheMethodofTheintegralequationsconstructedintheprecedingsectioncanbesolvedwithadequatenumericalmethods.Oneofthemostcommonlyusedmethodsinsolvingintegralequationsisthemethodofmoments(MoM)introducedbyR.F.Harringtonin1968[5].TeralprincipleandkeypointsofMoMwillbereviewedinthissection.…GeometricalModelingandDiscretizationofFromthedescriptionintheprecedingsection,itisclearthatinordertosolvefortheunknownequivalentelectromagneticcurrentsdefinedonthesurfaceorinthevolumeofanobstruction,thedefinitionoftheunknowncurrents,whichisthegeometry,needstobedescribedmathematically.Thisistheso-calledgeometricalmodeling.Incomputationalelectromagnetics,geometricalmodelingisthebasicofelectromagneticmodelingandnumericalcalculation,anditsqualitywillaffecttheaccuracyofthenumericalsolutiondirectly.…PlanarTriangularThesimplestandmostcommonlyusedelementinthegeometricalmodelingistheplanartriangle,whichisdefinedbyitsthreevertices(nodes).…CurvilinearTriangularThecurvedsurfaceofanobjectcanbebettermodeledwithcurvilineartriangularelementswhicharethesecond-ordercurvedsurfaces.Acurvilineartrianglecanbedefinedbysixnodes,threeofwhicharetheverticesofthetriangle,theotherthreearethemidpointsofthreecurvededges.ShowninFigure2-1isthesketchofacurvilineartriangularelement.Thecurvedsurfaceofanobjectcanbebettermodeledwithcurvilineartriangularelementswhicharethesecond-ordercurvedsurfaces.Acurvilineartrianglecanbedefinedbysixnodes,threeofwhicharetheverticesofthetriangle,theotherthreearethemidpointsofthreecurvededges.ShowninFigure2-1isthesketchofatriangularFigure2-1Thesketchofacurvilineartriangular（a）Thecurvilineartriangleinthecoordinatesystem;(b)ThecurvilineartriangleinthecoordinatesystemUsingthefollowingcoordinatetransformation,thecurvilineartriangleintherectangularcoordinatesystem,asshowninFigure2-1(a),canbemappedontothetriangledefinedinaparametriccoordinatesystem,asshowninFigure2-1(b)6r(1,2)j(1,2,3j

(2-where

denotetherectangularcoordinatesofthesixcontrollingnodesin2-

1，2，3aretheparametriccoordinatesvaryingfrom0to1,andtheysatisfy

123

(2-From(2-2),itisclearthatonlytwovariablesoutofthesethreeare…TheChoiceofBasisAfterthegeometricaldiscretizationoftheobjectsurfaceusingplanarorcurvilineartriangularelements,basisfunctionscanbedefinedonthesetriangularelementstoexpandtheunknownvectorfunctions.…PlanarRWGBasisIntroducedbyRaoWilton,andGlissonin1982,theRWGbasisfunction[6]isdefinedovertwoadjacenttriangularelements.①…CurvilinearRWGBasisInordertogiveabetterrepresentationofcurvedsurfaces,thecurvilineartriangularelementscanbeused.Correspondingly,thecurvilinearRWGbasisfunctions[7]canbedefinedonthecurvilineartriangularelements.…TheSolutionofMatrixThematrixequationcanbesolvedwithtwotypesofalgorithms,thedirectalgorithmsandtheiterativealgorithms.Theywillbeintroducedbrieflyinthissubsection[8].…DirectThecommonlyuseddirectalgorithmsincludetheGaussianelimination,theLUposition,andthesingularvalue position(SVD)[9-10].…IterativeWhenthedimensionoftheimpedancematrixisverylarge,thedirectsolutionesveryexpensive.……①Chapter3Calder?nPreconditioneratMidTheintegralequations(IEs)areusedtomodeltheelectromagnetic…Calder?nRelationandCalder?nInascatteringproblem,accordingtothesurfaceequivalence…Calder?nPreconditioneratMidBasedonthediscussioninthepreceding…TwosimpleexamplesaregiventodemonstratethefastconvergenceoftheCalder?npreconditioneratmidfrequencies.…TheCalder?npreconditionerfortheEFIEatmidfrequenciesisreviewedinthis…Chapter4Calder?nPreconditioningTechniqueforN-ysisoflow-frequencyelectromagneticproblemshasreceivedmore…N-MüllerIntegralConsidertheproblemofelectromagneticwavescatteringbyaconducting…Theorem1Considertheproblemofelectromagneticwavescatteringbyaconducting…theproblemis TheDerivationofN-MüllerThederivationbeginsfromthepreconditioningofthe…TheDiscretizationofN-MüllerThederivationbeginsfromthepreconditioningofthe…Inthissection,theperformanceoftheN-M¨ullerequationsis…Inthis…Chapter5TheaccurateandefficientnumericalsolutionsoftheMaxwell’sequationshaveimportantsignificancetotheysisofelectromagneticscatteringandradiation…Theresearchesreportedinthisdissertationhavecoveredmostimportantareasincludingtheconvergenceaccelerationofthe-kindintegralequationsandtheaccuracyimprovementofthesecond-kindintegralequationsforboththePECandthedielectriccases.Nevertheless,duetothetimelimitation,therearestillspacesforthefuturedevelopmentoftheCalder′on-technique-relatedmethods.…Onthecompletionofthis…[1]W.C.Chew,J.M.Jin,E.Michielssen,etal..FastandEfficientAlgorithmsinComputationalElectromagnetic[M].Boston:ArtechHouse,2000/r/